Tan Calculator — Tangent of Any Angle
Enter an angle in degrees or radians to get tan(θ) instantly — alongside sin(θ), cos(θ), cot(θ), sec(θ) and csc(θ) — with a plotted tangent curve showing the asymptotes.
Angle unit
Tangent — opposite ÷ adjacent in a right triangle; can be any real number
- 1
Convert to radians
45 × π ÷ 180 = 0.785398 - 2
sin(θ)
sin(0.785398) = 0.707107 - 3
cos(θ)
cos(0.785398) = 0.707107 - 4
tan(θ)
0.707107 ÷ 0.707107 = 1
How does this calculator work?
tan(θ) = sin(θ)/cos(θ) = opposite/adjacent. It is unbounded (any real value), undefined at odd multiples of 90°, and repeats every 180° (π rad). Odd function: tan(−θ) = −tan(θ). Key values: tan(0°)=0, tan(30°)=1/√3≈0.577, tan(45°)=1, tan(60°)=√3≈1.732, tan(90°) undefined.
Formula
How this is calculated
The tangent of angle θ equals the ratio of the opposite side to the adjacent side in a right triangle, or equivalently sin(θ) / cos(θ) on the unit circle. Because cosine equals zero at 90°, 270°, and every odd multiple of 90°, the tangent is undefined at those angles — its value increases without bound toward ±∞ as the angle approaches an asymptote.
Unlike sine and cosine, which oscillate between −1 and 1, the tangent function is unbounded: it can take any real value. The function repeats with period π (180°), half that of sine and cosine, so a single branch spans only 180° before the pattern restarts. Degree inputs are converted to radians (θ_rad = θ° × π / 180) before evaluation.
The plot shows the tan(θ) curve over three periods centred on your angle. Each continuous branch is drawn as a separate segment that ends just before the vertical asymptote. The companion values — sin, cos, cot = 1/tan, sec = 1/cos, csc = 1/sin — are all defined from the same unit-circle point and are shown in the stat grid.
Frequently asked questions
tan(θ) = sin(θ) / cos(θ). At exactly 90°, cos(90°) = 0, making the denominator zero and the ratio undefined. Geometrically, the tangent line at 90° is vertical — it never intersects the x-axis, so there is no finite value.
Tangent repeats every 180° (π radians): tan(θ + 180°) = tan(θ). This is half the period of sine and cosine (360° / 2π). Each branch lies between two consecutive asymptotes, which are 180° apart.
Tangent is odd: tan(−θ) = −tan(θ). Its graph has 180°-rotational symmetry about the origin. This follows from sin being odd and cos being even: tan(−θ) = sin(−θ)/cos(−θ) = −sin(θ)/cos(θ) = −tan(θ).
Also known as
TG we-Calculate Editorial Team. (2026). Tan Calculator — Tangent of Any Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/tan-calculator
TG we-Calculate Editorial Team. "Tan Calculator — Tangent of Any Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/tan-calculator.
TG we-Calculate Editorial Team, "Tan Calculator — Tangent of Any Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/tan-calculator
@misc{wecalculate_tan_calculator, title = {Tan Calculator — Tangent of Any Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/tan-calculator}}, year = {2026}, note = {TG we-Calculate} }
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